71=2n^2-1

Solution for 71=2n^2-1 equation:

Simplifying
71 = 2n2 + -1

Reorder the terms:
71 = -1 + 2n2

Solving
71 = -1 + 2n2

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-2n2' to each side of the equation.
71 + -2n2 = -1 + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
71 + -2n2 = -1 + 0
71 + -2n2 = -1

Add '-71' to each side of the equation.
71 + -71 + -2n2 = -1 + -71

Combine like terms: 71 + -71 = 0
0 + -2n2 = -1 + -71
-2n2 = -1 + -71

Combine like terms: -1 + -71 = -72
-2n2 = -72

Divide each side by '-2'.
n2 = 36

Simplifying
n2 = 36

Take the square root of each side:
n = {-6, 6}